Definite Integration Question 340
Question: $ \int_3^{8}{\frac{2-3x}{x\sqrt{(1+x)}}}dx $ is equal to
[Pb. CET 2001]
Options:
A) $ 2\log ( 3/2e^{3} ) $
B) $ \log (3/e^{3}) $
C) $ 4\log (3/e^{3}) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ \int_3^{8}{\frac{2-3x}{x\sqrt{1+x}}dx=I} $
Put $ 1+x=t^{2}\Rightarrow dx=2tdt $
When $ x=3\to 8, $ then $ t=2\to 3 $
$ I=2\int_2^{3}{\frac{5-3t^{2}}{t^{2}-1}dt} $ ; $ I=2\int_2^{3}{( \frac{2}{t^{2}-1}-3 )}dt $
$ I=2[ \frac{2}{2.1}\log \frac{t-1}{t+1}-3t ]_2^{3} $ ; $ I=2\log ( \frac{3}{2e^{3}} ) $ .
BETA
